1. Field of the Invention
The invention pertains generally to the field of collisions avoidance and more particularly to the indication of an area of danger, the perimeter of which is an exact representation of a desired miss distance between vehicles.
2. Basic components of a system for avoiding collisions between a vehicle, such as a ship, and other vehicles in its vicinity (collision avoidance systemxe2x80x94CAS) are an apparatus for detecting ships (targets) in the vicinity of the ship, namely a radar, and a system that displays relevant target information. Target information is displayed so that a human operator can realize collision potential and determine a collision avoidance course of action.
CAS systems of the prior art have incorporated synthetically generated symbology on the radar display that provides collision avoidance information with respect to areas of possible collisions (predicted areas of dangerxe2x80x94PADS) between own ship and radar detected targets. Range of a target from own ship and its relative bearing, determined by the radar, provide coordinates (R,xcex8) of a polar coordinate system with own ship at the center. These coordinates are transformed on to a Carterian x-y grid on which the target is positioned at P0, the transformation providing the coordinates at (R sin xcex8,R cos xcex8). Own ship""s heading may be added to xcex8 to obtain the true bearing of the target, which may be substituted for the relative bearing to realize the familiar North-East plane of the local North-East-Down (NED) system. By tracking changes in R and xcex8 of the target relative to own ship, estimates of range rate of change {dot over (R)} and bearing rate of change {dot over (xcex8)} may be projected at points along own ships track. The relative velocity between a target and own ship may then be estimated by the vector Vrel= less than {dot over (R)},{dot over (xcex8)} greater than . While R, xcex8, and {dot over (xcex8)} may vary with time, CAS assumes that the target velocity remains constant until own ship maneuvers.
A prior art CAS is described in U.S. Pat. No. 3,717,873 issued Feb. 20, 1973 to Riggs entitled xe2x80x9cShip""s Maneuver Assessment Systemxe2x80x9d. Riggs determines a predicted point of collision (PPC). Own ship""s speed vs. In space and time, is represented by a cone given by:
x2+y2=(vst)2
where t is the vertical axis of the cone and x and y are vxt and vyt, respectively. The target""s initial position P0 and velocity VT determine a straight line in space given by the vector equation
{overscore (P)}(t)=P0+{overscore (V)}Tt
A PPC is any point of intersection of this line with the cone. Depending upon the courses and speeds, there may be zero, one, or two PPCs for a given target. As long as own ship""s course does not take it through any of the target""s PPCs, a collision is not possible.
It is desirable to miss a target by a predetermined minimum distance. Riggs displays this minimum distance with a circle, having a radius equal to the minimum distance, centered about the PPC. This representation is true only if the target ship is stationary. When the target and own ship are moving, the boundary of the protected area also moves, distorting the boundary, which is actually kidney shaped.
A CAS that addresses the shortcoming of the circle centered about a PPC is described in U.S. Pat. No. 3,725,918 issued Apr. 3, 1973 to Fleischer, et al entitled xe2x80x9cA Collision Avoidance Display Apparatus For Maneuverable Craftxe2x80x9d. The patent describes the determination of a predicted area of danger (PAD), the boundary of which is approximated on a display by an ellipse surrounding the PPC. One axis of the ellipse runs along the target""s predicted track, thereby establishing the other axis perpendicular to the track. The width of the ellipse along the perpendicular axis, minor axis of the ellipse, is twice the predetermined miss distance RM. End points of the ellipse on the axis along the target ship""s track, major axis of the ellipse, are determined by relating the miss distance to the relative velocity between own ship and a target, determining the direction own ship must take to realize the miss distance, establishing the cross-over of own ship traveling in this direction with the target""s track, and determining the distance between the target and the cross-over point. Fore and aft crossover points are determined, the distance between these points being the major axis of the ellipse.
Synthetic symbology, such as ellipses, are drawn on a radar display during the flyback or deadtime of the azimuth sweeps. This requires separate circuitry and display deflection elements, such as deflection coils or plates in the cathode ray tube, for the display of the ellipses. These disadvantages were overcome by the invention disclosed in U.S. Pat. No. 4,224,621, issued to J. A. Cornett, et al on Sep. 23, 1980. As described in this patent, the analog radar returns are digitized and a full frame of data is stored and displayed in accordance with the scanning rate of radar antenna. The synthetic symbology is displayed with the radar data utilizing the same deflection circuitry used for displaying the radar data. Instead of utilizing ellipses to designate the PADs, however, the synthetic symbology comprises straight line segments which form a hexagon. Generating the synthetic symbology in this manner provides a saving in software since the display of an ellipse requires more software than does the display of a hexagon.
As implemented in the prior art, the PAD boundaries are only approximations of the true boundaries. In these implications, the dimensions and positions of the PADs change as the target ship and own ship traverse their routes. Due to the approximations of the PAD boundaries made in the prior art, as own ship approaches the path of a target that is slower than own ship, the major axis of the PAD decreases and becomes undefined as own ship crosses the target""s path. As own ship steams away from the path, the PAD again is defined and the major axis begins to expand. A classic case is that of a target that is faster than own ship. Such a target has two PADs. As own ship approaches the targets predicted path in the region between these PADs the distance between the PADs decreases. When the predicted path of the target is crossed the PADs overlap, indicating a collision danger even though none exists.
The above delineated disadvantages of the prior art are overcome by the present invention by establishing the boundary of a true PAD. When own ship intercepts a point on this boundary it will at the desired miss distance from the position of the target at the time of the boundary intercept.
A miss distance circle having a radius equal to the desired miss distance is generated about the initial position of the target and the coordinates of selected points on this miss distance circle and the distances of these selected points from own ship are respectively determined. Each of these selected points has a heading and velocity equal to that of the target. Points of intercept by own ship for these selected points are established utilizing the determined coordinates, the initial distance from own ship of each selected point, the target heading and speed, and the speed of own ship. A smooth curve is then drawn through the points of intercept to establish the boundary of the predicted area of danger (PAD).